Labour’s under-par performance in the local elections goes “much deeper” than poor management of expectations although the Conservatives have problems in the south of England, experts have said.

Veteran Tory pollster Lord Hayward said Jeremy Corbyn’s struggles with anti-Semitism in the party and criticism over his response to the Salisbury poisoning and the alleged chemical weapons attack in Syria had damaged Labour’s prospects in recent weeks.

In a mixed set of results, the party performed well in London but failed to take Tory flagship councils as many had predicted, while seeing gains in some areas around the country and falling back elsewhere.

Lord Hayward told The Yorkshire Post: “In local elections because the turnout is relatively low you often win elections by those of your opponents who don’t turn out to vote, and I think there’s clear evidence, less so in London, but on a nationwide basis - places like Leeds and Wakefield etc, that traditional Labour voters have been turned off voting for the Labour Party.”

The peer said Prime Minister Theresa May would see Thursday’s polls as an achievement for the Tories, while warning her not to be complacent.

“Little change for a party that’s a year into Government and eight years into an austerity programme is a striking achievement,” he said.

“There are still clearly problems in London because the younger, better educated, richer communities have apparently left the Tory Party and the Tory Party will have to get them back, probably post-Brexit.”

Ian Warren, who runs the Election Data blog and used to work for Labour, said the Tories’ approach to Brexit was causing damage in the South because a million people have left London in the last four years, and are mostly educated 30-something Remainers settling in the South East, East Anglia and the M4 corridor towards Bristol.

“They are 2:1 Remain and they vote Labour, so it means that a million people are spilling out into the South who are friendly to Labour," he said.

“And at the same time you have that whole part of the country as well is just packed with Tory Remainers and we’ve seen in the general election but also in local elections as well, what they’re doing is staying at home because they are not satisfied with what they're getting from Theresa May, the tone of Brexit, and they certainly wouldn’t vote for Jeremy Corbyn so the rational choice for them is to stay at home.

“That gives and opportunity for the Lib Dems, gives an opportunity for Labour in some places.”

The Tories have performed well in a lot of Brexit-backing areas in the North, but Lord Hayward said: "I have been struck and I think everyone has been struck by how little Brexit has come up on the doorstep - there is a correlation between the Leave areas and Tory gains, there's no question about that, so that is a factor, but Brexit itself is something that did not come up.”

For Labour, Mr Warren said the results point to deep problems in traditional heartlands like Wigan, Bolton, Hull, Sheffield and Wakefield.

“The Tories might not be winning a lot of seats but even if they are not winning seats they are picking up 5, 10, 15, 20 per cent in really staunch Labour areas,” he said.

“There's no other way of interpreting that other than traditional Labour voters are starting to go to the Conservatives or have gone to the Conservatives and have stayed there.”

Mr Warren also warned that while Labour may be performing well in some areas which make up key general election marginals, such as Dudley North, there are others where “it’s not good at all” such as Pudsey, Bolton West and Southampton Itchen.

Mr Warren said: “The marginals are just nowhere near good enough and if they have any hope of forming of a government you have to be winning those marginals.”

Mr Corbyn has blamed unrealistic expectations of how Labour would fare for the sense of disappointment as results come in.

But Lord Hayward said: “It is deeper than that.

“It is the fact that in places like Wakefield and Leeds and Dudley and Walsall and Nuneaton and Derby, the Labour Party has failed to take advantage of a late Conservative Government in difficulty and therefore the question has to be asked: why has Labour failed to take advantage?

“So there are questions for the Tory Party but there are bigger questions for the Labour Party.”